
pwd()

"C:\\Users\\user"


using Pkg


using LightGraphs
using MatrixNetworks
using VegaDatasets
using DataFrames
using SparseArrays
using LinearAlgebra
using Plots
using VegaLite


airports = dataset("airports")


typeof(airports)

VegaDatasets.VegaDataset


describe(DataFrame(airports))


flightsairport = dataset("flights-airport")


describe(DataFrame(flightsairport))


names(DataFrame(flightsairport))

3-element Vector{String}:
 "origin"
 "destination"
 "count"


typeof(flightsairport)

VegaDatasets.VegaDataset


flightsairportdf = DataFrame(flightsairport)


allairports = vcat(flightsairportdf[!, :origin], flightsairportdf[!, :destination])
uairports = unique(allairports)

305-element Vector{String}:
 "ABE"
 "ABI"
 "ABQ"
 "ABY"
 "ACK"
 "ACT"
 "ACV"
 "ACY"
 "ADK"
 "ADQ"
 "AEX"
 "AGS"
 "AKN"
 ⋮
 "TYR"
 "TYS"
 "VLD"
 "VPS"
 "WRG"
 "WYS"
 "XNA"
 "YAK"
 "YKM"
 "YUM"
 "CYS"
 "OGD"


# create ab airports data frame that has a subset of airports that are only included in the routes dataset
airportsdf = DataFrame(airports)
subsetairports = map(i -> findfirst(airportsdf[!, :iata] .== uairports[i]), 1:length(uairports))
airportsdf_subset = airportsdf[subsetairports, :]


# 인접행렬 만들기(Build the adjacency matrix)
ei_ids = findfirst.(isequal.(flightsairportdf[!, :origin]), [uairports])

5366-element Vector{Int64}:
   1
   1
   1
   1
   1
   1
   1
   1
   1
   1
   2
   3
   3
   ⋮
 300
 300
 300
 301
 301
 302
 303
 303
 303
 303
 303
 303


ej_ids = findfirst.(isequal.(flightsairportdf[!, :destination]), [uairports])

5366-element Vector{Int64}:
  19
  30
  62
  64
  74
  88
 151
 163
 211
 220
  82
  16
  19
   ⋮
 240
 261
 268
  54
 152
 268
 115
 143
 156
 158
 221
 268


edgeweights = flightsairportdf[!, :count]

5366-element Vector{Int64}:
  853
    1
  805
  465
  247
  997
    3
    9
 1425
    2
 2660
  368
 1067
    ⋮
    1
    1
    4
  363
  362
  340
    1
  326
   99
 1044
 1961
  440


A = sparse(ei_ids, ej_ids, 1, length(uairports), length(uairports))

305×305 SparseMatrixCSC{Int64, Int64} with 5366 stored entries:
⠀⠀⣾⠀⠁⡀⡂⠄⡃⢘⢚⣈⢒⢀⠀⠀⠀⢒⠀⢸⡒⡅⠐⣒⠀⠠⡒⢚⢚⠀⠀⠀⠐⡰⠰⠖⠀⡒⠀⠀
⠚⠛⢾⠓⠲⡒⡖⠓⠖⢺⢻⢻⢺⡶⠂⠗⠒⠿⠖⢺⣿⠖⠒⠶⠶⠚⡟⠻⢿⠒⠐⠗⢖⢛⢺⡒⠒⠞⠒⠆
⠠⠀⣸⠢⠪⠂⠧⠰⠷⢺⢹⠸⢸⠰⠲⠢⠁⢻⠄⠸⠷⠇⠐⢿⠾⠀⡷⢺⠾⠇⠘⠷⠴⠸⢸⠸⠄⠇⠀⠀
⠈⠌⢼⠁⠉⡓⠁⠀⡉⢸⢹⣸⢘⡘⠀⠈⠀⢹⠋⢉⠻⡋⠈⢻⢉⢀⡋⢹⠉⠉⠉⠉⢋⢸⠼⠉⠀⠋⠀⠄
⣫⢈⣸⣁⣹⣃⣃⣈⣏⣸⣹⣹⣘⢍⡀⣚⠀⣼⡃⣘⣿⣏⢸⣻⣻⢈⡏⣿⣻⡍⢈⣋⣫⣨⣸⣝⢙⣋⣁⡀
⡺⢐⣿⣒⣓⡒⣓⣒⣗⣺⣺⣺⣛⢒⡒⣖⠒⣻⣂⣒⣻⣾⢚⣳⣺⢒⡗⣻⣲⡒⢒⣖⣚⣐⣲⢚⣐⣛⡒⡒
⠘⢐⢺⡒⢒⡒⣒⠐⡖⢘⢻⢘⢀⠑⠀⡒⠐⣛⣂⢒⣿⡖⢰⣚⣓⠰⣆⢿⢻⣃⣒⣓⡺⢺⢸⢺⢒⡚⠆⠢
⠀⠀⢬⠀⠐⡀⠀⠀⡀⢨⢸⢬⢀⠠⠀⠁⠤⢠⠀⢀⠳⡃⠀⣩⣨⠨⡗⢺⠺⠀⠀⡒⠑⠸⠸⠂⠀⠝⠀⠀
⢠⢀⣼⡀⣤⣠⣌⣀⣀⣤⣼⣠⣴⢠⠀⣀⢀⣴⡀⣼⣤⣢⣠⣤⣀⡀⣧⣼⣤⣄⣀⣀⣤⢠⣸⣤⣀⣤⣀⡀
⢀⢀⣸⣡⣀⡁⡇⢈⣁⢩⢨⢸⢨⢘⠀⠀⣀⣬⡄⢨⣻⣁⢈⣿⡉⠀⣧⣩⣊⡁⣄⣁⣋⢈⣩⣈⣀⣃⡀⡃
⡘⠨⢻⠛⠽⠇⡻⠠⡿⣿⣿⢾⢻⠿⠽⠢⠠⣻⠟⢺⣎⠝⠘⣿⡿⠺⣿⢿⣿⠇⠋⠿⢿⢻⢻⣿⠄⠿⠬⠇
⢰⢠⢸⡄⣼⣄⣦⣀⣶⣲⢾⣰⣰⢰⡄⣠⠀⣾⣧⣴⣶⣴⢠⡶⣶⣐⣗⣾⣶⣦⢤⣦⣶⢰⣸⣲⠠⣶⣄⡀
⠂⠀⢸⠣⠚⠃⠃⠀⡛⢘⢺⣚⢘⠚⠂⡚⠀⠸⠃⠈⣻⡃⢘⢻⢐⠑⡇⣾⢙⡃⠈⡫⢚⢸⢘⠘⠁⠓⠁⠁
⣸⢈⣿⡉⣽⣃⣏⣈⣏⣭⣽⣭⣬⣝⣹⣍⣉⣿⡉⣻⣿⣻⣹⣽⣩⣩⣵⣿⣿⣁⣉⣹⣹⣹⣹⣯⣈⣹⣁⡁
⠘⠐⢻⠓⠚⠇⠇⠀⡟⠺⢸⠺⠻⢲⠘⠖⠀⢻⠊⠸⠿⠟⠸⣿⠷⠘⠟⢻⠾⠃⠓⠛⠞⢺⢸⠓⠚⡗⡀⠂
⠀⠀⢰⠆⢴⡆⡆⠀⡦⢱⢸⢰⢸⢹⢀⠅⠀⢸⠄⢸⣯⡄⠠⣷⡤⢀⣇⣹⣽⡀⠀⡀⢰⢸⢸⡢⠀⢆⠋⠄
⢐⡀⣾⢑⣐⡣⣋⣐⡋⣺⢚⢸⣚⣎⢑⡀⠀⣛⡋⢘⣷⣓⢘⣛⣟⣰⣗⣺⣻⣁⣀⣒⢐⣲⣰⣚⠀⣓⡀⠀
⢰⠆⢺⠲⣚⡒⡖⠃⣖⢾⣸⢚⢲⢒⠳⠂⠒⣾⡂⢺⣿⣶⢲⣺⣒⠐⡷⣾⢶⠓⠳⡲⣰⢺⣺⣾⠂⣲⠗⠒
⢠⠠⣸⠆⠤⠇⠴⠀⡧⢰⣴⢰⣸⠰⢄⡄⠀⣴⠤⢸⣤⡅⢠⣦⠥⢀⣆⣰⢾⠤⡠⢄⢤⢠⢨⣠⠠⠆⠁⡀
⠀⠀⠸⠀⠌⠀⠠⠄⠁⠼⠸⠨⠨⠄⠀⠄⠀⠸⠠⠠⠦⠇⠈⠹⠄⠀⠅⠸⠠⠀⠂⠄⠀⠀⠼⠀⠁⠀⠀⠀


A = max.(A, A')

305×305 SparseMatrixCSC{Int64, Int64} with 5668 stored entries:
⠀⠀⣾⠀⠁⡂⡂⠄⡋⢚⢚⣊⢒⢀⠀⠀⠀⢒⠀⢸⡒⡍⠐⣒⠈⠠⡒⢚⢚⠀⠀⠀⠐⡰⠰⠖⠀⡒⠀⠀
⠚⠛⢾⠓⠲⡚⡖⠓⠖⢺⢻⢻⢺⡶⠂⠗⠒⠿⠖⣺⣿⠖⠒⠶⠶⡚⡟⠻⢿⠒⠰⠗⢞⢛⢺⡒⠲⠞⠒⠆
⠡⠠⣸⠢⠪⠂⢧⠰⠷⢺⢹⠸⢸⠰⠲⠢⠁⣻⠄⠸⠷⠇⠒⢿⠾⠀⡷⢻⠾⠇⠸⠷⠴⡸⢺⠸⠤⠇⠂⠁
⠈⠌⢼⠉⢉⡓⠁⠀⡉⢸⢹⣸⢘⡘⠀⠈⠂⢹⡋⢉⠻⡋⠈⢻⢉⢀⡋⢹⠉⠉⠉⠉⢋⢸⠼⠉⠐⠋⠀⠆
⣫⢈⣸⣁⣹⣃⣃⣈⣏⣹⣹⣹⣘⢍⡀⣚⠀⣼⡇⣘⣿⣯⢸⣻⣻⢈⡏⣿⣻⡍⢌⣋⣫⣨⣸⣝⢙⣋⣁⡄
⡺⢰⣿⣒⣓⡒⣓⣲⣗⣺⣺⣺⣛⢒⡒⣖⠒⣻⣂⣒⣻⣿⢚⣳⣺⢲⡗⣿⣲⡒⢒⣖⣚⣐⣲⢚⣐⣛⡒⡒
⠘⢐⢺⡶⢒⡒⣒⠰⡖⢜⢻⢘⢄⠑⠀⡒⠐⣛⣂⢒⣿⡖⢰⣚⣳⠰⣆⢿⢻⣃⣖⣓⡺⢾⢸⢺⢒⡚⠆⠦
⠀⠀⢬⠄⠸⡂⡀⠀⣠⢨⢸⢬⢠⠠⠄⠁⠤⢠⠀⢀⠳⡃⠀⣩⣨⠨⡗⢾⢺⠄⠄⡖⠑⠸⠹⠂⠀⠽⠀⠄
⢠⢀⣼⡄⣥⣠⣌⣀⣀⣤⣼⣠⣴⢠⠀⣃⢀⣴⡀⣼⣤⣢⣠⣤⣀⡀⣧⣼⣤⣄⣀⣀⣤⢠⣸⣤⣀⣤⣀⡀
⣀⣀⣸⣡⣀⡁⡏⢈⣉⢩⢨⢸⢨⢘⠀⢀⣀⣬⡄⣩⣻⣁⢉⣿⡉⠀⣧⣩⣊⡁⣄⣁⣋⢈⣩⣈⣀⣃⡀⡃
⡜⠬⢻⠟⠽⠇⡿⠢⡿⣿⣿⣾⢻⠿⠽⠢⠠⣻⠟⢺⣎⠝⢘⣿⡿⠺⣿⣿⣿⠇⠋⠿⢿⢻⢻⣿⠄⠿⠬⠇
⢰⢠⢸⡄⣼⣄⣦⣀⣶⣲⢾⣰⣰⢲⡄⣠⠀⣾⣧⣴⣶⣴⢠⡶⣶⣐⣗⣾⣶⣦⢤⣦⣶⢰⣸⣲⠠⣶⣆⡀
⠂⡀⣸⠣⠚⠃⠃⢐⡛⢚⢺⣚⢙⡚⡂⡚⠀⠸⠃⠈⣻⡋⢘⢻⢔⠑⡇⣾⣙⡃⠈⣫⢛⣹⢘⠘⠁⢓⠁⠁
⣸⢈⣿⡉⣽⣋⣏⣈⣯⣭⣽⣭⣬⣝⣹⣍⣉⣿⡍⣻⣿⣿⣹⣽⣩⣭⣵⣿⣿⣁⣍⣹⣹⣹⣹⣯⣈⣹⣁⡁
⠚⠐⢻⠓⠾⠇⡇⠀⡟⠾⢸⠺⠿⢲⠚⠖⠀⢿⠎⠸⠿⠟⠸⣿⠷⠸⠟⢻⠾⠃⠓⠻⠟⢺⢼⠓⠚⡗⡀⠂
⠀⠀⢴⠆⢶⡆⡇⠀⡦⢱⢸⢴⢼⢹⢠⠥⠀⢸⠄⢹⣯⡄⠠⣷⡦⣠⣇⣹⣽⡀⠀⡠⢰⢸⢹⡢⠀⢎⠋⠄
⢐⡠⣾⢑⣐⡣⣋⣐⡋⣺⢚⢸⣺⣎⣑⡀⠀⣛⡋⢘⣿⣓⢘⣛⣟⣰⣗⣺⣻⣁⣐⣒⢰⣲⣰⣚⠀⣓⡀⠀
⢰⠆⢺⠲⣚⡒⡖⠃⣖⢾⣸⢚⣲⣒⠳⠂⠒⣾⡃⢺⣿⣶⢲⣺⣒⠐⡷⣾⢶⠓⠳⡲⣰⢺⣺⣾⠂⣲⠗⠓
⢠⠠⣸⠆⠤⠇⡴⠀⡷⢰⣴⢸⣸⠰⣄⡄⠀⣼⠤⢸⣤⡅⢠⣦⢥⢀⣆⣸⢾⠤⡠⢄⢤⢠⢨⣠⠠⠆⠁⡀
⠀⠀⠸⠄⠌⠀⠠⠄⠁⠼⢸⠨⠨⡅⠀⠄⠀⠸⠤⠨⠦⠇⠈⠹⠅⠀⠅⠸⠠⠈⠋⠄⠀⠈⢽⠁⠁⠠⠀⠀


spy(A) # sparse 행렬을 그래프로 보여줌


issymmetric(A)

true


L = SimpleGraph(A) # A type representing an undirected graph.

{305, 2834} undirected simple Int64 graph


# SimpleGraph 실습
G = SimpleGraph(10)
add_edge!(G, 7, 5)
add_edge!(G, 3, 5)
add_edge!(G, 5, 2)

true


cc = scomponents(A)

MatrixNetworks.Strong_components_output([1, 1, 1, 1, 1, 1, 1, 1, 1, 1  …  1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [305], 1, MatrixNetwork{Int64}(305, [1, 13, 15, 56, 57, 60, 61, 67, 70, 71  …  5619, 5626, 5628, 5629, 5656, 5658, 5659, 5665, 5667, 5669], [19, 30, 62, 64, 74, 88, 151, 163, 168, 188  …  115, 143, 156, 158, 221, 268, 81, 268, 101, 268], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1  …  1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))


# the degree distribution
degrees = sum(A, dims = 2)[:]
p1 = plot(sort(degrees, rev = true), ylabel = "log degree", legend = false, yaxis =:log)


p2 = plot(sort(degrees, rev = true), ylabel = "degree", legend = false)


plot(p1, p2, size = (600, 300))


maxdegreeid = argmax(degrees)

19


uairports[maxdegreeid]

"ATL"


us10m = dataset("us-10m")

Vega JSON Dataset


@vlplot(width = 500, height = 300) +
@vlplot(
    mark = {
        :geoshape,
        fill =:lightgray,
        feature =:states
    },
    data = {
        values = us10m,
        format = {
            type=:topojson,
            feature=:states
        }
    },
    projection = {type =:albersUsa},
) +
@vlplot(
    :circle,
    data = airportsdf_subset,
    projection={type=:albersUsa},
    longitude = "longitude:q",
    latitude = "latitude:q",
    size ={value = 10},
    color = {value =:steelblue}
) +
@vlplot(
    :rule,
    data=flightsairport,
    transform=[
        {filter = {field=:origin, equal=:ATL}},
        {
            lookup=:origin,
            from={
                data = airportsdf_subset,
                key=:iata,
                fields=["latitude", "longitude"]
            },
            as=["origin_latitude", "origin_longitude"]
        },
        {
            lookup=:destination,
            from={
                data=airportsdf_subset,
                key=:iata,
                fields=["latitude", "longitude"]
            },
            as = ["dest_latitude", "dest_longitude"]
        }
    ],
    projection = {type=:albersUsa},
    longitude="origin_longitude:q",
    latitude="origin_latitude:q",
    longitude2="dest_longitude:q",
    latitude2="dest_latitude:q"
)


ATL_paths = dijkstra(A, maxdegreeid)

([1.0, 2.0, 1.0, 1.0, 2.0, 2.0, 2.0, 1.0, 2.0, 2.0  …  1.0, 1.0, 3.0, 2.0, 1.0, 3.0, 2.0, 2.0, 2.0, 2.0], [19, 82, 19, 19, 151, 82, 270, 19, 17, 17  …  19, 19, 154, 268, 19, 54, 268, 221, 268, 268])


?dijkstra

search: dijkstra dijkstra_shortest_paths

compute shortest paths using Dijkstra's algorithm.
d = dijkstra(A,u) computes the shortest path from vertex u to all nodes 
reachable from vertex u using Dijkstra's algorithm for the problem.  
The graph is given by the weighted sparse matrix A, where A(i,j) is 
the distance between vertex i and j.  In the output vector d, 
the entry d[v] is the minimum distance between vertex u and vertex v.
A vertex w unreachable from u has d(w)=Inf.
pred is the predecessor tree to generate the actual shorest paths. 
In the predecessor tree pred[v] is the vertex preceeding v in the 
shortest path and pred[u]=0. Any unreachable vertex has pred[w]=0 as well.  
If your network is unweighted, then use bfs instead.

# Find the minimum travel time between Los Angeles (LAX) and
# Rochester Minnesota (RST).

(A,xy,labels) = load_matrix_network_metadata("airports")
A = -A; # fix funny encoding of airport data
lax = 247; rst = 355
(d,pred) = dijkstra(A,lax)
@printf("Minimum time: %d",d[rst]); #Print the path
@printf("Path:")
u = rst
while(u != lax)
    @printf("%s <-- ", labels[u])
    u = pred[u];
    if (u == lax)
        @printf("%s", labels[lax])
    end
end


typeof(ATL_paths)

Tuple{Vector{Float64}, Vector{Int64}}


ATL_paths[1][maxdegreeid]

0.0


maximum(ATL_paths[1])

3.0


@show stop1 = argmax(ATL_paths[1]) # 최대값의 인덱스를 반환
@show uairports[stop1];

stop1 = argmax(ATL_paths[1]) = 123
uairports[stop1] = "GST"


@show stop2 = ATL_paths[2][stop1]
@show uairports[stop2];

stop2 = (ATL_paths[2])[stop1] = 152
uairports[stop2] = "JNU"


@show stop3 = ATL_paths[2][stop2]
@show uairports[stop3];

stop3 = (ATL_paths[2])[stop2] = 259
uairports[stop3] = "SEA"


@show stop4 = ATL_paths[2][stop3]
@show uairports[stop4];

stop4 = (ATL_paths[2])[stop3] = 19
uairports[stop4] = "ATL"


# 미국지도를 나타내주는 그래프

using VegaLite, VegaDatasets

us10m = dataset("us-10m")
airports = dataset("airports")

@vlplot(width = 800, height=500) +
@vlplot(
    mark={
        :geoshape,
        fill="#eee",
        stroke=:white
        },
    data={
        values=us10m,
        format={
            type =:topojson,
            feature=:states,
            }
        },
    projection = {type =:albersUsa}
    )


# 점을 뿌리는 그래프

@vlplot(
    :circle,
    data  = airportsdf_subset,
    projection={type =:albersUsa},
    longitude="longitude:q",
    latitude="latitude:q",
    size={value=5},
    color={value=:gray}
)


# 최단 경로를 선으로 나타내 주는 그래프 

@vlplot(
    :line,
    data={
        values=[
            {airport=:ATL, order=1},
            {airport=:SEA, order=2},
            {airport=:JNU, order=3},
            {airport=:GST, order=4}
            ]
        },
    transform=[{
        lookup=:airport,
        from={
            data=airports,
            key =:iata,
            fields=["latitude", "longitude"]}
    }],
    projection={type=:albersUsa},
    longitude="longitude:q",
    latitude="latitude:q",
    order={field=:order, type=:ordinal}
)


using VegaLite, VegaDatasets

us10m = dataset("us-10m")
airports = dataset("airports")

@vlplot(width =600, height=400) +
@vlplot(
    mark={
        :geoshape,
        fill="#eee",
        stroke=:white
        },
    data={
        values=us10m,
        format={
            type =:topojson,
            feature=:states,
            }
        },
    projection = {type =:albersUsa}
    ) +  # 미국지도를 나타내주는 그래프
@vlplot(
    :circle,
    data  = airportsdf_subset,
    projection={type =:albersUsa},
    longitude="longitude:q",
    latitude="latitude:q",
    size={value=5},
    color={value=:gray}
) + # 점을 뿌리는 그래프
@vlplot(
    :line,
    data={
        values=[
            {airport=:ATL, order=1},
            {airport=:SEA, order=2},
            {airport=:JNU, order=3},
            {airport=:GST, order=4}
            ]
        },
    transform=[{
        lookup=:airport,
        from={
            data=airports,
            key =:iata,
            fields=["latitude", "longitude"]}
    }],
    projection={type=:albersUsa},
    longitude="longitude:q",
    latitude="latitude:q",
    order={field=:order, type=:ordinal}
) # 최단 경로를 선으로 나타내 주는 그래프


nodeid = argmin(degrees)

4


nodeid = argmin(degrees)
@show uairports[nodeid]
d = dijkstra(A, nodeid)
argmax(d[1]), uairports[argmax(d[1])]

uairports[nodeid] = "ABY"

(123, "GST")


function find_path(d, id)
    shortestpath = zeros(Int, 1+Int.(d[1][id]))
    shortestpath[1] = id
    for i = 2:length(shortestpath)
        shortestpath[i] = d[2][shortestpath[i-1]]
    end
    return shortestpath
end

find_path (generic function with 1 method)


p = find_path(d, 123)

5-element Vector{Int64}:
 123
 152
  17
  19
   4


uairports[p]

5-element Vector{String}:
 "GST"
 "JNU"
 "ANC"
 "ATL"
 "ABY"


?mst_prim

search: mst_prim mst_prim_matrix

compute a minimum spanning tree with Prim's algorithm.
T = mst_prim_matrix(A) computes a minimum spanning tree T using Prim's algorithm
for the spanning tree of a graph with non-negative edge weights.

T = mst_prim_matrix(A,false) produces an MST for just the component at A containing
vertex 1.  T = mst_prim_matrix(A,0,u) produces the MST for the component
containing vertex u.

(ti,tj,tv,nverts) = mst_prim(A) returns the edges from the matrix and does not
convert to a sparse matrix structure.  This saves a bit of work and is
required when there are 0 edge weights.

A = load_matrix_network("airports")
A = -A #convert to travel time
A = max.(A,A')
A = sparse(A)
(ti,tj,tv,nverts) = mst_prim(A)


ti, tj, tv, nverts = mst_prim(A)

([2, 3, 4, 5, 6, 7, 8, 9, 10, 11  …  296, 297, 298, 299, 300, 301, 302, 303, 304, 305], [66, 286, 19, 151, 82, 197, 19, 17, 17, 19  …  19, 182, 231, 268, 141, 54, 268, 156, 268, 101], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1  …  1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 305)


# 데이터 프레임으로 변환
df_edges = DataFrame(:ei => uairports[ti], :ej => uairports[tj])


@vlplot(width=600, height=400) +
@vlplot(
    mark={
        :geoshape,
        fill="#eee",
        stroke=:white
    },
    data={
        values=us10m,
        format={
            type=:topojson,
            feature=:states
        }
    },
    projection={type=:albersUsa},
) + # 미국 지도를 나타내는 플랏
@vlplot(
    :circle,
    data=airportsdf_subset,
    projection={type=:albersUsa},
    longitude="longitude:q",
    latitude="latitude:q",
    size={value=20},
    color={value=:gray}
) + # 공항 노드를 써클로 나타내는 플랏
@vlplot(
    :rule,
    data=df_edges, #data=flightsairport,
    transform=[
        {
            lookup=:ei,
            from={
                data=airportsdf_subset,
                key=:iata,
                fields=["latitude", "longitude"]
            },
            as=["originx", "originy"]
        },
        {
            lookup=:ej,
            from={
                data=airportsdf_subset,
                key=:iata,
                fields=["latitude", "longitude"]
            },
            as=["destx", "desty"]
        }
    ],
    projection={type=:albersUsa},
    longitude="originy:q",
    latitude="originx:q",
    longitude2="desty:q",
    latitude2="destx:q"
) # 최소스패닝 트리를 그리는 플랏


?MatrixNetworks.pagerank

pagerank(A,alpha) 
            # return the standard PageRank vector 
            # with uniform teleportation and alpha=0.85 
            # computed to machine precision


v = MatrixNetworks.pagerank(A, 0.85)

305-element Vector{Float64}:
 0.0020923348051623326
 0.0009436892155004145
 0.006119901015186467
 0.0006607117011710984
 0.0008603728281911192
 0.0006445871130434956
 0.0015924822798577083
 0.0009129198498983633
 0.0007673129766872152
 0.0007673129766872152
 0.0009549149040574479
 0.0010558743385657198
 0.0013344573507603737
 ⋮
 0.0006445871130434956
 0.0027593013724303977
 0.0006607117011710984
 0.001475388547065869
 0.0017187137444043738
 0.0006494983427307581
 0.0043517606900941854
 0.0016096866743709605
 0.0006494983427307581
 0.0015555904158222685
 0.0007866027711239782
 0.0008103673010237374


sum(v)

0.9999999999999999


insertcols!(airportsdf_subset, 7, :pagerank_value => v)


names(airportsdf_subset)

8-element Vector{String}:
 "iata"
 "name"
 "city"
 "state"
 "country"
 "latitude"
 "pagerank_value"
 "longitude"


@vlplot(width=500, height=300) +
@vlplot(
    mark={
        :geoshape,
        fill="#eee",
        stroke=:white
    },
    data={
        values=us10m,
        format={
            type=:topojson,
            feature=:states
        }
    },
    projection={type=:albersUsa},
) # 미국 지도를 나타내 주는 그래프


@vlplot(
    :circle,
    data=airportsdf_subset,
    projection={type=:albersUsa},
    longitude="longitude:q",
    latitude="latitude:q",
    size="pagerank_value:q",
    color={value=:steelblue}
) # 페이지 랭크 값의 크기만큼 버블을 키워주는 그래프


@vlplot(width=500, height=300) +
@vlplot(
    mark={
        :geoshape,
        fill="#eee",
        stroke=:white
    },
    data={
        values=us10m,
        format={
            type=:topojson,
            feature=:states
        }
    },
    projection={type=:albersUsa},
) + # 미국 지도를 나타내 주는 그래프
@vlplot(
    :circle,
    data=airportsdf_subset,
    projection={type=:albersUsa},
    longitude="longitude:q",
    latitude="latitude:q",
    size="pagerank_value:q",
    color={value=:steelblue}
) # 페이지 랭크 값의 크기만큼 버블을 키워주는 그래프


?clustercoeffs

search: clustercoeffs dirclustercoeffs global_clustering_coefficient

compute undirected clustering coefficients for a graph. clustercoeffs(A) computes a 
normalized, weighted clustering coefficients from a graph represented by a symmetric 
adjacency matrix A. clustercoeffs(A,weighted,normalized), with weighted and normalized 
boolean values indicating whether the computation has to be weighted and/or normalized.

A = load_matrix_network("clique-10")    
cc = clustercoeffs(MatrixNetwork(A))


cc = clustercoeffs(A)
cc[findall(cc.<=eps())] .= 0
cc

305-element Vector{Float64}:
 0.8333333333333334
 1.0
 0.6475609756097561
 0.0
 0.6666666666666666
 0.0
 0.5333333333333333
 1.0
 0.0
 0.0
 1.0
 1.0
 1.0
 ⋮
 0.0
 0.9779411764705882
 0.0
 1.0
 0.0
 0.0
 0.5897435897435898
 0.0
 0.0
 0.6666666666666666
 1.0
 1.0


insertcols!(airportsdf_subset,7,:ccvalues=>cc)


@vlplot(width=500, height=300) +
@vlplot(
    mark={
        :geoshape,
        fill="#eee",
        stroke=:white
    },
    data={
        values=us10m,
        format={
            type=:topojson,
            feature=:states
        }
    },
    projection={type=:albersUsa},
) +
@vlplot(
    :circle,
    data=airportsdf_subset,
    projection={type=:albersUsa},
    longitude="longitude:q",
    latitude="latitude:q",
    size="ccvalues:q",
    color={value=:gray}
) # size를 clustering coefficients를 사용함

iata	name	city	state	country	latitude	longitude
"00M"	"Thigpen"	"Bay Springs"	"MS"	"USA"	31.9538	-89.2345
"00R"	"Livingston Municipal"	"Livingston"	"TX"	"USA"	30.6859	-95.0179
"00V"	"Meadow Lake"	"Colorado Springs"	"CO"	"USA"	38.9457	-104.57
"01G"	"Perry-Warsaw"	"Perry"	"NY"	"USA"	42.7413	-78.0521
"01J"	"Hilliard Airpark"	"Hilliard"	"FL"	"USA"	30.688	-81.9059
"01M"	"Tishomingo County"	"Belmont"	"MS"	"USA"	34.4917	-88.2011
"02A"	"Gragg-Wade"	"Clanton"	"AL"	"USA"	32.8505	-86.6115
"02C"	"Capitol"	"Brookfield"	"WI"	"USA"	43.0875	-88.1779
"02G"	"Columbiana County"	"East Liverpool"	"OH"	"USA"	40.6733	-80.6414
"03D"	"Memphis Memorial"	"Memphis"	"MO"	"USA"	40.4473	-92.227
⋮	⋮	⋮	⋮	⋮	⋮	⋮

	variable	mean	min	median	max
	Symbol	Union…	Any	Union…	Any
1	iata		00M		ZZV
2	name		Abbeville Chris Crusta Memorial		Zephyrhills Municipal
3	city		Abbeville		Zuni
4	state		AK		WY
5	country		Federated States of Micronesia		USA
6	latitude	40.0365	7.36722	39.4344	71.2854
7	longitude	-98.6212	-176.646	-93.5994	145.621

	iata	name	city	state	country
	String	String	String	String	String
1	ABE	Lehigh Valley International	Allentown	PA	USA
2	ABI	Abilene Regional	Abilene	TX	USA
3	ABQ	Albuquerque International	Albuquerque	NM	USA
4	ABY	Southwest Georgia Regional	Albany	GA	USA
5	ACK	Nantucket Memorial	Nantucket	MA	USA
6	ACT	Waco Regional	Waco	TX	USA
7	ACV	Arcata	Arcata/Eureka	CA	USA
8	ACY	Atlantic City International	Atlantic City	NJ	USA
9	ADK	Adak	Adak	AK	USA
10	ADQ	Kodiak	Kodiak	AK	USA
11	AEX	Alexandria International	Alexandria	LA	USA
12	AGS	Bush	Augusta	GA	USA
13	AKN	King Salmon	King Salmon	AK	USA
14	ALB	Albany Cty	Albany	NY	USA
15	ALO	Waterloo Municipal	Waterloo	IA	USA
16	AMA	Amarillo International	Amarillo	TX	USA
17	ANC	Ted Stevens Anchorage International	Anchorage	AK	USA
18	ASE	Aspen-Pitkin Co/Sardy	Aspen	CO	USA
19	ATL	William B Hartsfield-Atlanta Intl	Atlanta	GA	USA
20	ATW	Outagamie County Regional	Appleton	WI	USA
21	AUS	Austin-Bergstrom International	Austin	TX	USA
22	AVL	Asheville Regional	Asheville	NC	USA
23	AVP	Wilkes-Barre/Scranton Intl	Wilkes-Barre/Scranton	PA	USA
24	AZO	Kalamazoo County	Kalamazoo	MI	USA
25	BDL	Bradley International	Windsor Locks	CT	USA
26	BET	Bethel	Bethel	AK	USA
27	BFL	Meadows	Bakersfield	CA	USA
28	BGM	Binghamton Regional	Binghamton	NY	USA
29	BGR	Bangor International	Bangor	ME	USA
30	BHM	Birmingham International	Birmingham	AL	USA
⋮	⋮	⋮	⋮	⋮	⋮

	iata	name	city	state	country
	String	String	String	String	String
1	ABE	Lehigh Valley International	Allentown	PA	USA
2	ABI	Abilene Regional	Abilene	TX	USA
3	ABQ	Albuquerque International	Albuquerque	NM	USA
4	ABY	Southwest Georgia Regional	Albany	GA	USA
5	ACK	Nantucket Memorial	Nantucket	MA	USA
6	ACT	Waco Regional	Waco	TX	USA
7	ACV	Arcata	Arcata/Eureka	CA	USA
8	ACY	Atlantic City International	Atlantic City	NJ	USA
9	ADK	Adak	Adak	AK	USA
10	ADQ	Kodiak	Kodiak	AK	USA
11	AEX	Alexandria International	Alexandria	LA	USA
12	AGS	Bush	Augusta	GA	USA
13	AKN	King Salmon	King Salmon	AK	USA
14	ALB	Albany Cty	Albany	NY	USA
15	ALO	Waterloo Municipal	Waterloo	IA	USA
16	AMA	Amarillo International	Amarillo	TX	USA
17	ANC	Ted Stevens Anchorage International	Anchorage	AK	USA
18	ASE	Aspen-Pitkin Co/Sardy	Aspen	CO	USA
19	ATL	William B Hartsfield-Atlanta Intl	Atlanta	GA	USA
20	ATW	Outagamie County Regional	Appleton	WI	USA
21	AUS	Austin-Bergstrom International	Austin	TX	USA
22	AVL	Asheville Regional	Asheville	NC	USA
23	AVP	Wilkes-Barre/Scranton Intl	Wilkes-Barre/Scranton	PA	USA
24	AZO	Kalamazoo County	Kalamazoo	MI	USA
25	BDL	Bradley International	Windsor Locks	CT	USA
26	BET	Bethel	Bethel	AK	USA
27	BFL	Meadows	Bakersfield	CA	USA
28	BGM	Binghamton Regional	Binghamton	NY	USA
29	BGR	Bangor International	Bangor	ME	USA
30	BHM	Birmingham International	Birmingham	AL	USA
⋮	⋮	⋮	⋮	⋮	⋮

	iata	name	city	state	country
	String	String	String	String	String
1	ABE	Lehigh Valley International	Allentown	PA	USA
2	ABI	Abilene Regional	Abilene	TX	USA
3	ABQ	Albuquerque International	Albuquerque	NM	USA
4	ABY	Southwest Georgia Regional	Albany	GA	USA
5	ACK	Nantucket Memorial	Nantucket	MA	USA
6	ACT	Waco Regional	Waco	TX	USA
7	ACV	Arcata	Arcata/Eureka	CA	USA
8	ACY	Atlantic City International	Atlantic City	NJ	USA
9	ADK	Adak	Adak	AK	USA
10	ADQ	Kodiak	Kodiak	AK	USA
11	AEX	Alexandria International	Alexandria	LA	USA
12	AGS	Bush	Augusta	GA	USA
13	AKN	King Salmon	King Salmon	AK	USA
14	ALB	Albany Cty	Albany	NY	USA
15	ALO	Waterloo Municipal	Waterloo	IA	USA
16	AMA	Amarillo International	Amarillo	TX	USA
17	ANC	Ted Stevens Anchorage International	Anchorage	AK	USA
18	ASE	Aspen-Pitkin Co/Sardy	Aspen	CO	USA
19	ATL	William B Hartsfield-Atlanta Intl	Atlanta	GA	USA
20	ATW	Outagamie County Regional	Appleton	WI	USA
21	AUS	Austin-Bergstrom International	Austin	TX	USA
22	AVL	Asheville Regional	Asheville	NC	USA
23	AVP	Wilkes-Barre/Scranton Intl	Wilkes-Barre/Scranton	PA	USA
24	AZO	Kalamazoo County	Kalamazoo	MI	USA
25	BDL	Bradley International	Windsor Locks	CT	USA
26	BET	Bethel	Bethel	AK	USA
27	BFL	Meadows	Bakersfield	CA	USA
28	BGM	Binghamton Regional	Binghamton	NY	USA
29	BGR	Bangor International	Bangor	ME	USA
30	BHM	Birmingham International	Birmingham	AL	USA
⋮	⋮	⋮	⋮	⋮	⋮

Chapter 8. 그래프(Graphs)¶

(줄리아 학습 노트)¶

데이터 전처리¶

8.1 최다 빈도 연결점 시각화¶

2. 최단거리 찾기 문제 (Shortest path problem)¶

DIJKSTRA¶

Functions¶

Example¶

3. 최소 스패닝 트리 (Minimum Spanning Tree, MST)¶

MST_PRIM¶

Functions¶

Example¶

4. 페이지 랭크(page lank)¶

`pagerank`¶

Functions¶

Inputs¶

Examples¶

5. 군집 계수(Clustering Coefficients)¶

CLUSTERCOEFFS¶

Functions¶

Example¶

Finally...¶

🥳 One cool finding¶

origin	destination	count
"ABE"	"ATL"	853
"ABE"	"BHM"	1
"ABE"	"CLE"	805
"ABE"	"CLT"	465
"ABE"	"CVG"	247
"ABE"	"DTW"	997
"ABE"	"JFK"	3
"ABE"	"LGA"	9
"ABE"	"ORD"	1425
"ABE"	"PHL"	2
⋮	⋮	⋮

	origin	destination	count
	String	String	Int64
1	ABE	ATL	853
2	ABE	BHM	1
3	ABE	CLE	805
4	ABE	CLT	465
5	ABE	CVG	247
6	ABE	DTW	997
7	ABE	JFK	3
8	ABE	LGA	9
9	ABE	ORD	1425
10	ABE	PHL	2
11	ABI	DFW	2660
12	ABQ	AMA	368
13	ABQ	ATL	1067
14	ABQ	AUS	433
15	ABQ	BWI	546
16	ABQ	CLE	12
17	ABQ	CVG	260
18	ABQ	DAL	3078
19	ABQ	DEN	4318
20	ABQ	DFW	2888
21	ABQ	ELP	799
22	ABQ	EWR	167
23	ABQ	HOU	1011
24	ABQ	IAD	365
25	ABQ	IAH	2261
26	ABQ	LAS	2402
27	ABQ	LAX	2395
28	ABQ	LBB	366
29	ABQ	MAF	367
30	ABQ	MCI	670
⋮	⋮	⋮	⋮

Chapter 8. 그래프(Graphs)¶

(줄리아 학습 노트)¶

데이터 전처리¶

8.1 최다 빈도 연결점 시각화¶

2. 최단거리 찾기 문제 (Shortest path problem)¶

DIJKSTRA¶

Functions¶

Example¶

3. 최소 스패닝 트리 (Minimum Spanning Tree, MST)¶

MST_PRIM¶

Functions¶

Example¶

4. 페이지 랭크(page lank)¶

pagerank¶

Functions¶

Inputs¶

Examples¶

5. 군집 계수(Clustering Coefficients)¶

CLUSTERCOEFFS¶

Functions¶

Example¶

Finally...¶

🥳 One cool finding¶

`pagerank`¶